T owards Realistic Stringy Models of Particle Physics & - - PowerPoint PPT Presentation

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T owards Realistic Stringy Models of Particle Physics & - - PowerPoint PPT Presentation

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T owards Realistic Stringy Models of Particle Physics & Cosmology as viewed by Gary Shiu University of Wisconsin What is String Phenomenology? Particle Physics & Cosmology Deep connection, e.g., inflation, dark matter,

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T

  • wards Realistic Stringy Models
  • f Particle Physics & Cosmology

Gary Shiu

University of Wisconsin

as viewed by

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What is String Phenomenology?

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Particle Physics & Cosmology

  • Deep connection, e.g., inflation, dark matter, neutrinos...
  • Both study the universe in the extreme conditions.
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The Standard Model(s)

Hierarchy problem SUSY? ..... Flatness, horizon, anisotropy Inflation? Dark Energy? .....

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The Quiver Diagram

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The Quiver Diagram

Inflation, dark matter, ... Neutrinos, cosmic rays, ...

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The Quiver Diagram

CMB, graviational waves, ... B i g b a n g , d a r k e n e r g y , . . .

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The Quiver Diagram

C a l a b i

  • Y

a u , G 2 , . . . S U S Y , B r a n e W

  • r

l d , . . .

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The Quiver Diagram

String Phenomenology is the study of the links!

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Are we ready for String Phenomenology?

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The beginning of the unexpected ...

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String Theory as a model of hadrons

String theory began as a phenomenological model. Massless spin 2 particle: graviton!

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Lessons

  • Ideas driven by phenomenological questions.
  • Need explicit models (c.f. QFT versus the

Standard Model).

  • Fixing problems that plague the theory often

leads to new and far-reaching ideas:

  • --Extra spin-2 particle graviton
  • --Tachyon SUSY
  • Works better than expected.
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Meet the Quintuplets

Type I IIA IIB HO HE

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The Heterotic Supremacy

  • Type IIA/IIB: Difficult to implement non-

Abelian gauge groups and chiral fermions. In fact, a no-go theorem for constructing the Standard Model.

  • Heterotic E8xE8: naturally contains GUTs

(E6, SO(10), SU(5),...) and hidden sectors.

  • Type I and Heterotic SO(32): two other

siblings that are largely ignored ...

[Dixon, Kaplunovsky, Vafa]

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String Phenomenology Begins

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1985

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Calabi-Yau Compactification

  • Low energy physics (spectrum, couplings,...)

determined by topology & geometry of M.

  • Building realistic heterotic string models: a

huge industry beginning in the mid 80s. N=1 SUSY Calabi-Yau

Candelas, Horowitz, Strominger, Witten

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The Score Card

  • E6, SO(10), SU(5) GUTs & MSSM-like vacua.
  • Rank .
  • Constraints on gauge groups & matter reps.
  • Gauge unification.
  • Exotic matter: Schellekens’ theorem.

Internal consistencies + phenomenological constraints a very tight system! However, two nagging problems ...

≤ 22

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Moduli Problem

Varying the size & shape of M In 4D, this freedom implies moduli: scalar fields

V (φi) = 0 ∀φi φi

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Moduli Problem

  • Different give inequivalent physics

(e.g., couplings, particle masses, ...)

  • Existence of light scalars:
  • Equivalence principle violations.
  • Time varying .
  • Energy in can ruin cosmology.

φi α

Loss of predictivity Phenomenological problems

< φi >

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SUSY Breaking

  • Assumptions:
  • But ...
  • Non-perturbative effects (e.g., gaugino and/or ----
  • -matter condensate) break SUSY.
  • The same NP effects also lift all moduli.

SUSY breaking effects on SM and moduli lifting potential not computed in a controlled stringy way.

  • SUSY scale ~ TeV (hierarchy problem).
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1995

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“When you come to a fork in the road, take it.” Yogi Berra

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Return of the Lost Family

Type I Type IIB HE HO Type IIA

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The Post-1995 Picture

heterotic on CY3 M on G2 F on CY4 compactifications with flux intersecting branes large extra dimensions Horava!Witten

Worth taking a fresh look at these long-standing problems.

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All (new) roads lead to branes

“Open string” “Closed string” “D-brane” Duality between geometry and branes: M-theory on G2, F-theory on CY4, Horava-Witten, ...

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Brane World

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Open Strings

  • Pioneering work (before 1995)
  • Recent review articles

Bianchi, Pradisi, Sagnotti, ... Polchinski .... Angelantonj, Sagnotti Blumenhagen, Cvetic, Langacker, Shiu

Formalism: Model Building:

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Flux Compactification

  • Just like particle couples to gauge field via
  • Dp-brane couples to p+1 index gauge fields:
  • Thus p+2-form field strengths:
  • worldline

A

  • worldvolume

Ap+1

Fp+2 = dAp+1

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Flux Compactification

  • For each p-cycle in M, we can turn on
  • Analogous to turning on a B-field
  • Σp

Fp ∈ Z

Energy ∼ 1 8π E2 + B2

Various p!cycles of M

Dirac Quantization

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Moduli Stabilization

  • The energy cost of a given flux depends on

detailed geometry of M:

  • Lift moduli !

Vn1,n2,...,nk(φi)

nj =

  • Σj

F , j = 1, . . . , k.

where

φi

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Type IIB Flux Vacua

  • Superpotential induced by
  • Stabilizes the dilaton and complex structure

moduli (shape) of M.

  • Additional mechanism stabilizes the Kahler

moduli (size).

W =

  • M

G ∧ Ω G3 = F3 − τH3

Gukov, Vafa, Witten Dasgupta, Rajesh, Sethi Greene, Schalm, Shiu Taylor, Vafa Giddings, Kachru, Polchinski ... Kachru, Kallosh, Linde, Trivedi ...

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Flux Induced SUSY

3 D3 ISD G

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Flux Induced SUSY

3 D3 ISD G

No soft terms

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Flux Induced SUSY

D3 3 IASD G

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Flux Induced SUSY

D3 3 IASD G

Non-trivial soft terms Explicit calculations. Lust, Reffert, Stieberger

Camara, Ibanez, Uranga Grana, Grimm, Jockers, Louis

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Can the Standard Model fit into this picture?

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Chiral D-brane Models

  • Branes at singularities

D3!branes Calabi!Yau

Two known ways to obtain chiral fermions:

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  • Intersecting branes

Number of generations given by:

Πa Πb M

[Πa] ◦ [Πb] = topological

Type IIB (N,M) U(M) U(N) Type IIA Type IIB

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  • Intersecting branes/magnetized D-branes

Number of generations given by:

Πa Πb M

[Πa] ◦ [Πb] = topological

Type IIB (N,M) U(M) U(N) Type IIA

“T

  • ron”
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The Recipe

  • Pick your , and the associated sLAG
  • Chiral spectrum:
  • Tadpole cancellation (Gauss’s law):
  • K-theory constraints

Representation Multiplicity

a 1 2 (π a ◦ πa + πO6 ◦ πa) a 1 2 (π a ◦ πa − πO6 ◦ πa)

(

a, b)

πa ◦ πb (

a, b)

π

a ◦ πb

  • a

Na (Πa + Π

a) − 4ΠO = 0

M Πa

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K-theory Constraints

  • D-brane charges are classified by K-theory.
  • Discrete charges invisible in SUGRA, forbid

certain non-BPS branes to decay.

  • Uncanceled K-theory charges can manifest

as Witten anomalies on D-brane probes.

  • Implications to the statistics of string vacua.
  • Direct construction of such discrete charged

branes.

Minasian & Moore Witten Sen Uranga Blumenhagen et al Schellekens et al Maiden, Shiu, Stefanski

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T

  • ward Realistic D-brane Models
  • Many toroidal orbifold/orientifold models.
  • MSSM flux vacua.
  • D-branes in general Calabi-Yau (less is

known about supersymmetric ).

  • Gepner orientifolds

Πa

For a review, see, e.g., Blumenhagen, Cvetic, Langacker, Shiu, hep-th/0502005. Angelantonj, Bianchi, Pradisi, Sagnotti, Stanev Dijkstra, Huiszoon, Schellekens Blumenhagen, Weigard Marchesano, Shiu

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How about Cosmology?

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Inflation as a probe of stringy physics

  • Almost scale invariant, Gaussian primordial

spectrum predicted by inflation is in good agreement with data.

  • A tantalizing upper bound on the energy

density during inflation:

V ∼ M 4

GUT ∼ (1016GeV)4

i.e., H ∼ 1014GeV

WMAP

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Planckian Microscope?

1. 10. 100.
  • 1000. 10000.
  • 100000. 6
10 0.000107 0.000108 0.000109 0.00011

Easther, Greene, Kinney, Shiu Schalm, Shiu, van der Schaar

200 400 600 800 1000 1200 1400
  • 0.002
0.002 0.004 0.006 0.008 0.01 0.012

k

∆C C

  • P 1/2(k)
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Brane Inflation

Extra Brane Extra Anti! Brane Our Brane

Dvali and Tye

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Brane Inflation

Dvali and Tye

Extra Brane Extra Anti! Brane Our Brane

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Brane Inflation

+ F strings + D strings radiation Brane Our

Stringy signatures, e.g., gravitational waves ...

Tye et al Copeland, Myers, Polchinski ...

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Brane Inflation

Are the branes moving slowly enough? Is reheating efficient? Can the cosmic strings be stable?

Warping by Fluxes

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Warped Throats

  • Fluxes back-react on the metric:

5 UV AdS IR

e.g., Klebanov, Strassler

“warped deformed conifold”

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Warped Throats

D3 D3

DBI inflation

Silverstein and Tong

˙ φ2 ≤ f(φ)−1

Casual speed limit:

S = −

  • d4x√−g
  • f(φ)−1
  • 1 − f(φ) ˙

φ2 − V (φ) − f(φ)−1

  • γ =

1

  • 1 − f(φ) ˙

φ2

warp factor

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Warped Throats

  • Cosmic strings spatially separated from SM

branes: not susceptible to breakage.

  • Reheating via tunneling is efficient due to KK

versus graviton wavefunctions. Barneby, Burgess, Cline

Kofman and Yi Chialva, Shiu, Underwood Frey, Mazumdar, Myers

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Non-Gaussianities

0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 0.1 0.2 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 1 2 3 0.2 0.4 0.6 0.8

Large 3-point correlations that are potentially observable. Moreover, distinctive shape. Slow-roll DBI

[Figures from Chen, Huang, Kachru, Shiu]

−54 < fNL < 114 (WMAP3) fNL ∼ 5 (PLANCK)

(fNL ∼ ) (fNL ∼ γ2)

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Have we gone too far?

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The Landscape

How many string vacua are there?

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Number of vacua

!1 !k

Gauss’s law:

  • Σj

Fp = nj

N 2and k depend on the topology of M, roughly O(100).

# vacua ∼ N k

naively can exceed 10100

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Sightseeing in the Landscape

  • These are candidate vacua (very few known

examples where all moduli are stabilized.)

  • The open string landscape (relevant to

phenomenology!) is less understood.

  • Realistic models are rare (QFT vs the

Standard Model).

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Landscape: what is it good for?

Douglas et al Kachru et al Conlon & Quevedo Blumenhagen et al Schellekens et al

1 10 100 1000 10000 100000 1 2 3 4 5 6 7 8 9 Nr of solutions Nr of chiral families Standard model spectrum with 1 to 9 chiral families type 4 type 2 type 0 type 5 type 3 type 1

Dienes

!1 2 !

{12} "=4/3 {1} {3} {2}

{0}{1} {0}{2} {0}{3} {0}{13} {0} {0}{2} {3} {0} {0} {0}{1} {0} {0} {1}{2} {0}{2}{3} {23}

{3} {1}

Dienes, Dudas, Gherghetta

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The Wave Function?

Ψ ( )

Hartle, Hawking, Vilenkin, Linde, ...

In the context of string landscape

Sarangi, Tye Kane, Perry, Zytkow Ooguri, Vafa, Verlinde ...

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Summary

  • String phenomenology ~ 20+ year old baby
  • -not fully accomplished but no longer naive.
  • Too early for string phenomenology? Part of

the SM was developed before gauge theories were shown to be renormalizable.

  • Spin-off results (e.g., Calabi-Yau, G2, mirror

symmetry, duality, topology change, ...).

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Summary

  • Fountain of new ideas/scenarios for particle

physics and cosmology: SUSY: high/low, split, ... Extra dimensions: large/small, warped/unwarped,

  • ------------universal/brane world.

...... Brane universe: brane inflation, DBI inflation, ... Technicolor: AdS/CFT

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2005 +

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Thank you